Well this is what I did. I brought the coaches together to which the home coach said "jeremy, we have a new shot clock operator, and you will have to watch her"

I told both this. I KNOW that more than 7 seconds went off the clock and now since we have lost 10 seconds off the game clock, we are going to add 3 seconds to the game clock, and award the ball to the home team due to the visiting team allowing the shot clock to expire.

The clock was verified at 7, but a good couple seconds after the inbound, the operator reset. Yes, we should have caught it, and working with a couple relatively new NCAA rules officials, I should have looked again.

Lesson learned, and both coaches had no problem with the ruling.

It is simply using the principle of "definite knowledge" to reset the clock; you're not resetting the clock back to the original time, only back to the time where it was determined the violation occured. Then, as far as the "foul" is concerned, it would be no different than if you saw contact after the horn went off - you simply ignore it unless it was intentional or flagrant, since the violation occured first.

A retroactive dead ball? Do we do that for anything else 10 seconds after the fact?

How about an end-of-game scenario? Same play, but instead of the shot clock at 7, it's the game clock. After an amount of time (say, 17 seconds) with the ball inbounds, a foul occurs to send a player to the line with a chance to win the game. However, after checking the monitor, it was determined the clock started about 10 seconds after it should have, and the foul occured well after the 7 seconds that should've run off the game clock. Wouldn't the ruling be the same?

(Yes, I know the officials should be watching the clock, counting, etc. so that this shouldn't happen.)

Yes. When the "reset" shot clock expires.

So 'shot-clock period' refers to the 'new' shot clock and not the previous? 5-11.4 states "...may be corrected in the shot-clock period in which it occurred." ("it" being the mistake, not the discovery)

Jeremy handled it properly (kudos), but i'm confused by the wording.

I haven't researched enough to give a definitive answer, but it seems the norm for most situations is before the 2nd live ball. But then what about a situation where after the shot clock should have expired then there is an OOB to Team A and then there is 2nd dead ball while A is in possession and the mistake is realized?